Finite Group Databasebeta

← #20254239

Subgroups — #20254239

Order 6016.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689701C211yesmaximal, characteristic, complemented
2#15689689C211yesmaximal, characteristic, complemented
3#15689462C211yesmaximal, characteristic, complemented
4#15689446C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689434C211yesmaximal, characteristic, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689372C211yesmaximal, characteristic, complemented
9#15689358C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic, complemented
22#13094020—21no—
23#13094010—21no—
24#13094003—21no—
25#13094000C2211yescharacteristic
26#13094000C2211yescharacteristic, complemented
27#13093999C2211yescharacteristic
28#13093998—21no—
29#13093998C2211yescharacteristic
30#13093996—21no—
31#13093996—21no—
32#13093995C2211yescharacteristic
33#13093995C2211yescharacteristic
34#13093995C2211yescharacteristic, complemented
35#13093994—21no—
36#13093992—21no—
37#13093982C2211yescharacteristic
38C2×C4⋊Dic47C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093956C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47D411yescharacteristic
75C2×C22⋊D47D411yescharacteristic
76C22×Dic47—21no—
77D4×D47—41no—
78D4×D47—41no—
79#10625350—41no—
80#10625350—41no—
81C2×D188—21no—
82C2×D188D411yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×Dic94D411yescharacteristic
87SD16×C47—41no—
88D8×C47—41no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96#10625336—41no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112#10625324—41no—
113C8×D47—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C2×D411yescharacteristic
117C22×D47—21no—
118C22×D47—42no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47C2×D411yescharacteristic
122C22×D47C2×D411yescharacteristic
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—42no—
130D4×C47—81no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—42no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—41no—
139C22⋊D47—41no—
140C22⋊D47—42no—
141C22⋊D47—81no—
142C22⋊D47—81no—
143C22⋊D47—81no—
144C22⋊D47—81no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—81no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—41no—
154D188—81no—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—21no—
159Dic94—41no—
160C8×C47—21no—
161C8×C47—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47C22×D411yescharacteristic
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47H(5,𝔽2)11yescharacteristic
188C4×C47H(5,𝔽2)11yescharacteristic
189Dic47—21no—
190Dic47—21no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194#3198—471nomaximal, Sylow
195C2×C47—41no—
196C2×C47—81no—
197C2×C47—81no—
198C2×C47#53411yescharacteristic
199C2×C47#57611yescharacteristic
200C2×C47#57711yescharacteristic
201D47—41no—
202D47—41no—
203D47—81no—
204#537—471no—
205#535—471no—
206#485—471no—
207#482—471no—
208#481—471no—
209#480—471no—
210#469—471no—
211#468—471no—
212#466—471no—
213#465—471no—
214#450—471no—
215#449—471no—
216#449D4711yescharacteristic, complemented
217#447—471no—
218#408—471no—
219C47#319811yescharacteristic, complemented, Sylow
220C2×#41—471no—
221C2×#41C2×D4711yescharacteristic, complemented
222C22×D4—471no—
223C2×SD16—471no—
224C2×SD16C2×D4711yescharacteristic
225C2×D8—471no—
226C2×D8C2×D4711yescharacteristic
227C2×M16—471no—
228C22×C8—471no—
229#127—941no—
230#124—941no—
231C22⋊Q8—471no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—471no—
235#121—471no—
236#121—471no—
237#121—471no—
238#121—471no—
239#121—941no—
240#121—941no—
241#121—941no—
242#121C2×D4711yescharacteristic
243#120—941no—
244#120—941no—
245#117—471no—
246C2×C4⋊C4—471no—
247#107—471no—
248#107—471no—
249#106—471no—
250#106—471no—
251#103—471no—
252#103C2×D4711yescharacteristic, complemented
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102C2×D4711yescharacteristic, complemented
259C22⋊C8—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C22⋊C8C2×D4711yescharacteristic, complemented
263C24—941no—
264#41—41no—
265#41—41no—
266#41—1881no—
267#41—1881no—
268C2×Q8—471no—
269C2×Q8C22×D4711yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—471no—
273C2×D4—471no—
274C2×D4—471no—
275C2×D4—471no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—1881no—
283C2×D4—1881no—
284C2×D4C22×D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—21no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—941no—
290C22×C4C22×D4711yescharacteristic
291SD16—41no—
292SD16—1881no—
293D8—41no—
294D8—1881no—
295M16—1881no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—471no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C4⋊C4C22×D4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C42—941no—
318C23—21no—
319C23—21no—
320C23—471no—
321C23—471no—
322C23—941no—
323C23—3761no—
324C23—3761no—
325C23—1882no—
326C23D4×D4711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—1881no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—941no—
337D4—941no—
338D4—3761no—
339D4—3761no—
340D4—3761no—
341D4—3761no—
342D4—3761no—
343D4—1881no—
344D4—1881no—
345D4—1881no—
346D4—1882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—471no—
353C2×C4—471no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—3761no—
362C2×C4D4×D4711yescharacteristic
363C2×C4C23×D4711yescharacteristic
364C8—21no—
365C8—21no—
366C8—941no—
367C8—941no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—941no—
378C22—941no—
379C22—941no—
380C22—941no—
381C22—941no—
382C22—941no—
383C22—3764no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22C2×D4×D4711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—941no—
392C4—941no—
393C4—1881no—
394C4—1881no—
395C4—1881no—
396C4#1309406911yescharacteristic
397C4#1309406911yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—3761no—
402C2—1881no—
403C2—1881no—
404C2#1568968311yescharacteristic
405C2#1568992711yescharacteristic
406C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689701C2semidirect
2. #15689689C2semidirect
3. #15689462C2semidirect
4. #15689446C2semidirect
5. #15689442C2semidirect
6. #15689434C2semidirect
7. #15689373C2semidirect
8. #15689372C2semidirect
9. #15689358C2semidirect
10. #15689349C2semidirect
11. #15689272C2semidirect
12. #15689268C2semidirect
13. #15689255C2semidirect
14. #15689088C2semidirect
15. C47×#449C2semidirect
20. C2×#10625324C22semidirect
21. C2×C8×D47C22semidirect
26. #13094000C22semidirect
34. #13093995C22semidirect
38. C2×C4⋊Dic47C22semidirect
39. #13093957C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093956C22semidirect
43. #13093948C22semidirect
48. #13093945C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
52. C2×#41×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
216. #449D47semidirect
219. C47#3198semidirect
221. C2×#41C2×D47semidirect
252. #103C2×D47semidirect
258. #102C2×D47semidirect
262. C22⋊C8C2×D47semidirect